Abstract: An elastomeric member having one or more preformed, self-sealing slits and which and dilate at predetermined pressures to form a fluid flow path. In an undilated condition, reverse flow is prevented.In various embodiments, an elastomeric infusion manifold is disclosed having a plurality of self-sealing slits formed therein relative to either a center lumen, a center slit or in independent relation to one another. Individual, hole mounting, fingered compression-type clamps permit a one-handed connection to the manifold.In other embodiments, catheters are disclosed having lengthwise co-extensive self-sealing, flow channels, comprising slit containing core members, integral slit containing solid portions or solid core members mounted within the catheter lumen such that flow occurs in the space between the core and the catheter walls. Conventional leur lock connectors or compression-type clamp connectors are useable therewith.